Question: Solve for $x$ and $y$ using substitution. ${5x-6y = 3}$ ${y = -x+5}$
Solution: Since $y$ has already been solved for, substitute $-x+5$ for $y$ in the first equation. ${5x - 6}{(-x+5)}{= 3}$ Simplify and solve for $x$ $5x+6x - 30 = 3$ $11x-30 = 3$ $11x-30{+30} = 3{+30}$ $11x = 33$ $\dfrac{11x}{{11}} = \dfrac{33}{{11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {y = -x+5}\thinspace$ to find $y$ ${y = -}{(3)}{ + 5}$ $y = -3 + 5$ $y = 2$ You can also plug ${x = 3}$ into $\thinspace {5x-6y = 3}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ - 6y = 3}$ ${y = 2}$